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EIT image reconstruction requires an accurate inverse model to get the conductivity of distribution within the domain, which is often computed expensively, especially in three dimensional applications. Large linear systems should be inverted in calculation. In the paper a Node Jacobian Back-Project Algorithm is presented. We use a node Jacobian-based method scaling with the number of nodes in our algorithm rather than the traditional elemental method scaling with the number of elements. We validate the algorithm's performance in our FEM hemi-sphere model by comparing with the elemental method. In order to demonstrate its capability, the reconstruction images of the experimental phantom tests data are presented with our new Sensitivity Matrix.